Find the inverse of each function. Is the inverse a function? y=(x+4)³-1

The logarithmic form of 5⁻³ = 1/125 is , [tex]log_5(\frac{1}{125} ) =-3[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function or equation

           x define expression

Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms :

According to statement,

5⁻³ = 1/125

as, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex]

Here,

a= 5, x= -3, N = 1/125

therefore logarithmic form is :  [tex]log_5(\frac{1}{125} ) =-3[/tex]

To know more about logarithms, visit :

brainly.com/question/5956809

#SPJ4

Answer:

26

Step-by-step explanation:

[tex]2(4)^0+4! \\ \\ =2(1)+24 \\ \\ =26[/tex]

If the mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by y = 3.50x + 6.00, then the number of games you can bowl for $34 is equal to 8.

A linear function can be described as an equation in which the highest power of the variables is not more than 1. As the linear function given is;

y = 3.50x + 6.00

Here y represents the total cost and x represents the number of games played.

We can find the number of games you can bowl for $34 as follows;

y = 3.50x + 6.00

34 = 3.50(x) + 6.00

34 - 6.00 = 3.50(x)

28 = 3.50(x)

x = 28 ÷ 3.50

x = 8

Hence, the number of games you can bowl for using the equation y = 3.50x + 6.00 is calculated to be 8.

To learn more about linear functions, click here:

https://brainly.com/question/12983872

#SPJ4

Equation that has the specified asymptotes for the translation of y=2/x. x=4 and y=-8  is :

y = 2 / x- 4   -  8

The graph is shifted by that many units in the positive direction if you deduct a constant from your original function's x.

The original function's graph is shifted downward by that many units if a constant is subtracted from the y value.

Your first formula was y=2/x. The vertical asymptote is discovered when the denominator's root is solved for. It is x=0 in this instance, or the y-axis.

And when x changes to ∞, y=2/∞=0. This indicates that the y-axis, or your horizontal asymptote, is at y=0.

After seeing the first graph

Now, you can see the transformation of y=2/x below. As is evident, it has shifted 2 units to the right and 8 units down with vertical asymptote at x=4 and horizontal asymptote at y=−8.

you can see the second graph here...

Learn more about the equation for the translation of given asymptotes :

https://brainly.com/question/2702714

#SPJ4

x = 6 is the extraneous solution of the equation

The equation given is

[tex]\sqrt{3x + 7}[/tex] = x -1

To find the Extraneous solution we need to square on both sides of the equation

[tex](\sqrt{3x + 7} )^{2}[/tex] =[tex](x - 1)^{2}[/tex]

3x + 7 = [tex]x^{2}[/tex] --2x + 1

[tex]x^{2}[/tex] - 5x - 6 = 0

[tex]x^{2}[/tex] - 6x + x - 6 = 0

x(x - 6) +1(x -6) =0

(x-6)(x+1) = 0

x = -1, 6

Now we need to put the value of x in the equation

x = -1

[tex]\sqrt{(3 * -1) + 7}[/tex] = -1 -1

[tex]\sqrt{4}[/tex] = -2

2≠ -2

Now put

x = 6

[tex]\sqrt{3 * 6 + 7}[/tex] = 6 -1

[tex]\sqrt{25}[/tex] = 5

5=5

Therefore we get to know that x = -1 is the extraneous solution and x = 6 is the solution of the equation

To know more about the extraneous solution refer to the link given below:

      https://brainly.com/question/12361474

      #SPJ4

Answer: 140

Step-by-step explanation: 25x20=500

32x20=640

640-500= 140!!

Answer:

b) $1,391.25

Step-by-step explanation:

Noon is at 12pm, so 8am-12pm will be 4 hours.
8821-3256=5565, so the snack bar made $5565 in 4 hours, to find how much it made in 1 hour we need to divide 5565 by 4.

5565/4=1391.25

6t ÷ 9

I hope this helps!

Answer: 6t

Step-by-step explanation:

there are 6 t's so yea it's  the 6th work for me -_-

The value of logarithmic expression log 4 √47/5² is log (47/25)^1/4.

By considering the given  logarithmic expression

log 4 √47/5²

log  4 √47/25

log (47/25)^1/4

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

Learn more about logarithm here

brainly.com/question/25710806

#SPJ4

Answer:

0.2

Step-by-step explanation:

Divide 2 by 9. You’ll get 0.222222…

So, you have to round it down to 0.2

I hope this helps. Please mark me brainliest.

The sequence is -2 1/4, - 1.2, -0.7, 2 1/2, 2 3/4.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

We have given number as

-2 1/4 = -2.25

-1.2

-0.7

2.5

2.75

So, the arrangement from least to greatest is -2 1/4, - 1.2, -0.7, 2 1/2, 2 3/4.

Learn more about sequence here:

https://brainly.com/question/28615767

#SPJ1

Answer:

Step-by-step explanation:

the answer is 46.989

tenths, ones, decimal, hundredths, thousandths

the answer must be greater than 46.98 but less than 47.

The amount of fuel required to drive 250 miles will be 25.14 liters.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that a car consumes 25.00 liters of fuel when driving a distance of 400.0 km. The amount of fuel required for 250 miles will be calculated as:-

1 km = 0.6213 miles

400 km = 400 x 0.6213 miles

400 km = 248.52 miles

248.52 miles = 25 litres

1 mile = 25 / 248.52 litres

250 miles = ( 250 x 25 ) / 248.52 litres

250 miles = 25.14 litres

Therefore, the amount of fuel required to drive 250 miles will be 25.14 liters.

To know more about an expression follow

https://brainly.com/question/11280632

#SPJ1

Yes, the claim is correct because √16 + π = 4 + π and  4 + π  is an irrational number

Rational numbers are numbers that can be expressed as the ratio of two integers while Irrational numbers cannot be expressed as the ratio of two numbers.

The sum of a rational and an irrational number is always an irrational number.

Example:

Consider a rational number: 4 and an irrational number: 2.7582...

When we add these two numbers, we get,

4 + 2.7582... = 6.7582....

Thus, it is clear that this sum is also an irrational number as the numbers after decimal are non-terminating and non-recurring.

Thus, the correct option is that the claim is correct because √16 + π = 4 + π which is an irrational number

Read more about rational numbers at; https://brainly.com/question/12088221

#SPJ1

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.105ft2 is the area of given figure.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

The given figure has rectangle and semi circle.

Area of rectangle=length * Breadth

=10*8

=80 ft2

Area of semicircle=1/2πr2 (r=4ft)

=1/2*3.14*(4)^2

=3.14*4*2=25.12ft2

Therefore area of figure is

=Area of rectangle+Area of semicircle

=80ft2+25.12ft2

=105ft2.

Therefore area of figure is 105ft2.

To learn more on area click:

https://brainly.com/question/27683633

#SPJ1

The Approximate assessment probability that next year is temperature year 16 will be in the 90s is 0.53

In the image that we have, there are 8 years out of a total of 15 years that would be having the temperature in the 90s.

This can be written in the fraction as 8 / 15 = 0.53

The probability can be defined as the chances of having something happening.

Hence we would say that the Approximate assessment probability that next year is temperature year 16 will be in the 90s is 0.53

Read more on probability here:

https://brainly.com/question/24756209

#SPJ1

The proof that is correct about vertical angles being congruent is; Joby's proof

Vertical angles are defined as the angles formed when two lines meet each other at a point. They are always equal to each other and as such they are congruent.

Now, from the given image, we see that four angles are formed which are; ∠1, ∠2, ∠3, ∠4

Now, according to vertical angle theorem, we can say that;

∠2 = ∠4 and ∠1 = ∠3

Thus, we can conclude that vertical angles are congruent by the vertical angle theorem

Thus, we conclude that Joby's proof is correct.

Read more about Vertical Angles at; https://brainly.com/question/1673457

#SPJ1

Answer:

$58.32

Step-by-step explanation:

x = 1/3(79.26 + 95.70)

x = 1/3(147.96)  Divide 147.96 by 3

x = 58.32

x + 2 is the graph of the function g, whose graph is a horizontal reduction of the graph of f by a factor of 1/2.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

The translation is a way of changing the position of an object on a xy-plane.

The function that results from shrinking a function f(x) horizontally by a factor of 1/a is given as;

g(x) =1/a f(x)

Give the function f(x) = 2x + 4, which will result in the following function if the function is shortened horizontally:

g(x) = 1/2(2x+4)

g(x) = x + 2

Hence the function g whose graph is a horizontal shrink of the graph of f by a factor of 1/2 is x + 2.

Learn more on horizontal shrink here:

brainly.com/question/24816886

#SPJ1

The image of Quadrilateral ABCD after transformation is shown in graph with coordinates A' (0, 2), B' (2, 4), C' (5, 4) and D' (4, 3).

What is Transformation?

Transformation is the act or process of changing completely.

The rule of transformation is given as;

(x, y) --> (x-2, y+5)

Now, The coordinates of Quadrilateral ABCD are;

A (2, -3) , B (4, -1), C (7, -1) and D (6, -2)

Apply the rule of transformation to find the coordinates of the image of Quadrilateral ABCD as;

A' (2-2, -3+5) = (0, 2)

B' (4-2, -1+5) = (2, 4)

C' (7-2, -1+5) = (5, 4)

D' (6-2, -2+5) = (4, 3)

Hence, The coordinates of image of Quadrilateral ABCD are;

A' (0, 2), B' (2, 4), C' (5, 4) and D' (4, 3).

And, The image of Quadrilateral ABCD after transformation is shown in graph.

Learn more about the transformation visit:

https://brainly.com/question/1620969

#SPJ1

A potential exponential function (y = abˣ) that has a y-intercept of (0, 3) and passes through the point (2, 48) is equal to y = 3·4ˣ

An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be represented by this standard formula:

y = abˣ

Next, we would solve for the value of "a" using y-intercept (0, 3):

y = abˣ

3 = ab⁰

3 = a(1)

a = 3.

Also, we would determine the value of "b" from point (2, 48):

y = abˣ

48 = 3b²

16 = b²

b = √16

b = 4.

Substituting the parameters into the standard formula, we have;

y = 3·4ˣ

Read more on exponential functions here: https://brainly.com/question/26570390

#SPJ1

Answer:

B. 2(5+3)

Step-by-step explanation:

PEMDAS

2(5+3)

5+3= 8

2 × 8 = 16

10 + 6 = 16

Answer:

$690.63

Step-by-step explanation:

45 minutes = 0.75 hr, so he worked for 48.75 hrs.

This means he worked 8.75 hours of overtime, so his pay is

[tex]40(13)+(8.75)(13)(1.5) \approx \$690.63[/tex]

Since Jasmine wants to enter a career with median earnings of at least $33,500, but she doesn’t want to go to college, the occupation that fits her will be C Private detective.

It should be noted that from the information, Jasmine wants to enter a career with median earnings of at least $33,500, but she doesn’t want to go to college.

A Makeup artist earns $31,820.

A Mathematician earns $86,930.

A Private detective earns $33,750

A Massage therapist earns $33,400.

Therefore, the best occupation for her since she doesn't want to go to college and earns above $33500 is the private detective.

Learn more about occupation on:

brainly.com/question/1206328

#SPJ1

Answer:

C. Private detective

Step-by-step explanation:

Answer:transversal

Step-by-step explanation:

The simplified value of the expression is [tex]-2^{2/3}[/tex].

The cube root of any given number is that number which we can multiply 3 times by itself to get the original number. It is denoted by ∛, for example- the cube root of x will be ∛x. It can also be written as (x)^1/3.

Here, we are given the expression ∛4 - 2∛4

We can also write this expression as follows-∛4 (1 - 2)= ∛4(-1)= - ∛4

Further, 4 can be written as: 2 × 2 = 2² = - (∛2)² = [tex]-2^{2/3}[/tex]

We cannot simplify this expression any further.

Thus, the value of the expression comes out to be [tex]-2^{2/3}[/tex].

Learn more about cube roots here- https://brainly.com/question/2868097

#SPJ4

The statement which are true for triangle LMN are :

1 ) The angle at vertex L is acute.

2) The angle at vertex N is acute.

What is obtuse angle ?

An obtuse angle is defined as an angle measuring less than 180 degrees and greater than 90 degrees. Examples of obtuse angle degrees include 165°, 135°, 110°, 179°, 91°, etc., which lie between 90° and 180°.

Here, it is given that triangle LMN has an obtuse angle at vertex M that is :

The angle formed by vertex L and N will be acute angle that is less then 90 degrees as to satisfy the triangle law of addition (all sum of all the angles of a triangle is 180 degree).

Therefore, option A and D are correct.

check and know more about angles here :

https://brainly.com/question/7116550

#SPJ1

Answer:  1, 2 and 5

Step-by-step explanation:

Analyzing Obtuse Triangles
see picture

Answer: x=7

Step-by-step explanation: 15x=120, x=8, 8-1= 7 brainliest?

Answer:

1. y = 0.5x – 0.5 or y =  1/2x -1/2

2. y = -1.5x – 2   or  y= -3/2x- 2

3. y= -x -5

4. y=x+3

i dk how to do the last picture